Need to calculate:The factorization of 3p3−2p2−9p+6.

Question

Fatema Sutton · Accepted Answer

Formula used:
The factors of a polynomial can be found by taking a common factor and this method is called factor by grouping,

a b + a c + b d + c d = a (b + c) + d (b + c)

= (a + d) (b + c)

Or,

a b - a c + b d - c d = a (b - c) + d (b - c)

= (a + d) (b - c)

Calculation:
Consider the polynomial

3 p^{3} - 2 p^{2} - 9 p + 6

.
This is a four term polynomial, factorization of this polynomial can be found by factor by grouping as,

3 p^{3} - 2 p^{2} - 9 p + 6 = (3 p^{3} - 2 p^{2}) + (- 9 p + 6)

= p^{2} (3 p - 2) - 3 (3 p - 2)

As,

(3 p - 2)

is the common factor of the polynomial,
The polynomial can be factorized as,

3 p^{3} - 2 p^{2} - 9 p + 6 = p^{2} (3 p - 2) — 3 (3 p - 2)

= (3 p - 2) (p^{2} - 3)

Therefore, the factorization of the polynomial is

(3 p - 2) (p^{2} — 3)

.

Need to calculate:The factorization of 3p^{3}-2p^{2}-9p+6.